exponents

resilient · Posted: Thu Apr 10, 2008 11:58 pm Post subject: exponents

2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^10=

1. 2^10
2. 2^11
3. 2^18
4. 2^54
5. 2^56

oa is b? what is the shortest way to do this?

Neo2000 · Posted: Fri Apr 11, 2008 12:05 am Post subject:

2^n + 2^n = 2(2^n) = 2^(n+1)

Once you know this, you will realise that your answer is 2^11

p.s. 250 posts!!! Very Happy

cjiang16 · Posted: Sat Apr 12, 2008 4:49 pm Post subject:

Using estimation, the answer is B.

Stuart Kovinsky · Posted: Sat Apr 12, 2008 7:20 pm Post subject:

manju_ej · Posted: Mon Jul 21, 2008 8:23 am Post subject: Re: exponents

[quote="resilient"]2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^10=

1. 2^10
2. 2^11
3. 2^18
4. 2^54
5. 2^56

The answer is 2^11
Remove the first term (2) and take a look at the remaining portions. They are in the Geometric Progression.
So the formula to find the sum of n terms of a geometric progression is S=b1*(1-r^n/1-r), where b1 is the first term, r is the ratio between the two variables, in this case r=2 (ie, third term divided by second term)
By using this formula, I got S=2046.
Now add the term '2' we removed to this figure(s=2046) which gives you 2048.
We know 2^10 is 1024 so 2^10*2=2048.
So the answer is 2^10*2^1 ,which is equal to 2^11, option B.

sudhir3127 · Posted: Mon Jul 21, 2008 8:53 am Post subject:

i wud use goemetric mean to solve the problem..

reachac · Posted: Mon Jul 21, 2008 9:47 am Post subject:

I'd rather use sum of GP to solve.